MLPY/Lib/site-packages/sympy/physics/quantum/tests/test_qapply.py

from sympy.core.mul import Mul
from sympy.core.numbers import (I, Integer, Rational)
from sympy.core.singleton import S
from sympy.core.symbol import symbols
from sympy.functions.elementary.miscellaneous import sqrt

from sympy.physics.quantum.anticommutator import AntiCommutator
from sympy.physics.quantum.commutator import Commutator
from sympy.physics.quantum.constants import hbar
from sympy.physics.quantum.dagger import Dagger
from sympy.physics.quantum.gate import H, XGate, IdentityGate
from sympy.physics.quantum.operator import Operator, IdentityOperator
from sympy.physics.quantum.qapply import qapply
from sympy.physics.quantum.spin import Jx, Jy, Jz, Jplus, Jminus, J2, JzKet
from sympy.physics.quantum.tensorproduct import TensorProduct
from sympy.physics.quantum.state import Ket
from sympy.physics.quantum.density import Density
from sympy.physics.quantum.qubit import Qubit, QubitBra
from sympy.physics.quantum.boson import BosonOp, BosonFockKet, BosonFockBra


j, jp, m, mp = symbols("j j' m m'")

z = JzKet(1, 0)
po = JzKet(1, 1)
mo = JzKet(1, -1)

A = Operator('A')


class Foo(Operator):
    def _apply_operator_JzKet(self, ket, **options):
        return ket


def test_basic():
    assert qapply(Jz*po) == hbar*po
    assert qapply(Jx*z) == hbar*po/sqrt(2) + hbar*mo/sqrt(2)
    assert qapply((Jplus + Jminus)*z/sqrt(2)) == hbar*po + hbar*mo
    assert qapply(Jz*(po + mo)) == hbar*po - hbar*mo
    assert qapply(Jz*po + Jz*mo) == hbar*po - hbar*mo
    assert qapply(Jminus*Jminus*po) == 2*hbar**2*mo
    assert qapply(Jplus**2*mo) == 2*hbar**2*po
    assert qapply(Jplus**2*Jminus**2*po) == 4*hbar**4*po


def test_extra():
    extra = z.dual*A*z
    assert qapply(Jz*po*extra) == hbar*po*extra
    assert qapply(Jx*z*extra) == (hbar*po/sqrt(2) + hbar*mo/sqrt(2))*extra
    assert qapply(
        (Jplus + Jminus)*z/sqrt(2)*extra) == hbar*po*extra + hbar*mo*extra
    assert qapply(Jz*(po + mo)*extra) == hbar*po*extra - hbar*mo*extra
    assert qapply(Jz*po*extra + Jz*mo*extra) == hbar*po*extra - hbar*mo*extra
    assert qapply(Jminus*Jminus*po*extra) == 2*hbar**2*mo*extra
    assert qapply(Jplus**2*mo*extra) == 2*hbar**2*po*extra
    assert qapply(Jplus**2*Jminus**2*po*extra) == 4*hbar**4*po*extra


def test_innerproduct():
    assert qapply(po.dual*Jz*po, ip_doit=False) == hbar*(po.dual*po)
    assert qapply(po.dual*Jz*po) == hbar


def test_zero():
    assert qapply(0) == 0
    assert qapply(Integer(0)) == 0


def test_commutator():
    assert qapply(Commutator(Jx, Jy)*Jz*po) == I*hbar**3*po
    assert qapply(Commutator(J2, Jz)*Jz*po) == 0
    assert qapply(Commutator(Jz, Foo('F'))*po) == 0
    assert qapply(Commutator(Foo('F'), Jz)*po) == 0


def test_anticommutator():
    assert qapply(AntiCommutator(Jz, Foo('F'))*po) == 2*hbar*po
    assert qapply(AntiCommutator(Foo('F'), Jz)*po) == 2*hbar*po


def test_outerproduct():
    e = Jz*(mo*po.dual)*Jz*po
    assert qapply(e) == -hbar**2*mo
    assert qapply(e, ip_doit=False) == -hbar**2*(po.dual*po)*mo
    assert qapply(e).doit() == -hbar**2*mo


def test_tensorproduct():
    a = BosonOp("a")
    b = BosonOp("b")
    ket1 = TensorProduct(BosonFockKet(1), BosonFockKet(2))
    ket2 = TensorProduct(BosonFockKet(0), BosonFockKet(0))
    ket3 = TensorProduct(BosonFockKet(0), BosonFockKet(2))
    bra1 = TensorProduct(BosonFockBra(0), BosonFockBra(0))
    bra2 = TensorProduct(BosonFockBra(1), BosonFockBra(2))
    assert qapply(TensorProduct(a, b ** 2) * ket1) == sqrt(2) * ket2
    assert qapply(TensorProduct(a, Dagger(b) * b) * ket1) == 2 * ket3
    assert qapply(bra1 * TensorProduct(a, b * b),
                  dagger=True) == sqrt(2) * bra2
    assert qapply(bra2 * ket1).doit() == TensorProduct(1, 1)
    assert qapply(TensorProduct(a, b * b) * ket1) == sqrt(2) * ket2
    assert qapply(Dagger(TensorProduct(a, b * b) * ket1),
                  dagger=True) == sqrt(2) * Dagger(ket2)


def test_dagger():
    lhs = Dagger(Qubit(0))*Dagger(H(0))
    rhs = Dagger(Qubit(1))/sqrt(2) + Dagger(Qubit(0))/sqrt(2)
    assert qapply(lhs, dagger=True) == rhs


def test_issue_6073():
    x, y = symbols('x y', commutative=False)
    A = Ket(x, y)
    B = Operator('B')
    assert qapply(A) == A
    assert qapply(A.dual*B) == A.dual*B


def test_density():
    d = Density([Jz*mo, 0.5], [Jz*po, 0.5])
    assert qapply(d) == Density([-hbar*mo, 0.5], [hbar*po, 0.5])


def test_issue3044():
    expr1 = TensorProduct(Jz*JzKet(S(2),S.NegativeOne)/sqrt(2), Jz*JzKet(S.Half,S.Half))
    result = Mul(S.NegativeOne, Rational(1, 4), 2**S.Half, hbar**2)
    result *= TensorProduct(JzKet(2,-1), JzKet(S.Half,S.Half))
    assert qapply(expr1) == result


# Issue 24158: Tests whether qapply incorrectly evaluates some ket*op as op*ket
def test_issue24158_ket_times_op():
    P = BosonFockKet(0) * BosonOp("a") # undefined term
    # Does lhs._apply_operator_BosonOp(rhs) still evaluate ket*op as op*ket?
    assert qapply(P) == P   # qapply(P) -> BosonOp("a")*BosonFockKet(0) = 0 before fix
    P = Qubit(1) * XGate(0) # undefined term
    # Does rhs._apply_operator_Qubit(lhs) still evaluate ket*op as op*ket?
    assert qapply(P) == P   # qapply(P) -> Qubit(0) before fix
    P1 = Mul(QubitBra(0), Mul(QubitBra(0), Qubit(0)), XGate(0)) # legal expr <0| * (<1|*|1>) * X
    assert qapply(P1) == QubitBra(0) * XGate(0)     # qapply(P1) -> 0 before fix
    P1 = qapply(P1, dagger = True)  # unsatisfactorily -> <0|*X(0), expect <1| since dagger=True
    assert qapply(P1, dagger = True) == QubitBra(1) # qapply(P1, dagger=True) -> 0 before fix
    P2 = QubitBra(0) * QubitBra(0) * Qubit(0) * XGate(0) # 'forgot' to set brackets
    P2 = qapply(P2, dagger = True) # unsatisfactorily -> <0|*X(0), expect <1| since dagger=True
    assert qapply(P2, dagger = True) == QubitBra(1) # qapply(P1) -> 0 before fix
    # Pull Request 24237: IdentityOperator from the right without dagger=True option
    assert qapply(QubitBra(1)*IdentityOperator()) == QubitBra(1)
    assert qapply(IdentityGate(0)*(Qubit(0) + Qubit(1))) == Qubit(0) + Qubit(1)